Question

What is the ratio of diffusion rate of oxygen to hydrogen?
(a) $ 1:4 $
(b) $ 4:1 $
(c) $ 1:8 $
(d) $ 8:1 $

Answer 1

Hint :Diffusion is known as the movement of a substance from an area of high concentration to an area of low concentration. Diffusion is seen in liquids and gases because their particles move randomly from place to place. Rate of diffusion of a gas is inversely related to the square root of molar mass of a gas.
 $ \dfrac{{{r_1}}}{{{r_2}}} = \sqrt {\dfrac{{{M_2}}}{{{M_1}}}} $
 $ {r_1} = $ Rate of diffusion of oxygen
 $ {r_2} = $ Rate of diffusion of hydrogen
 $ {M_1} = $ Molecular weight of oxygen
 $ {M_2} = $ Molecular weight of hydrogen

Complete Step By Step Answer:
 $ {M_1} = 32g $ of $ {O_2} $
 $ {M_2} = 2g $ of $ {H_2} $
Substituting the values in the formula we get,
 $ \dfrac{{{r_1}}}{{{r_2}}} = \sqrt {\dfrac{2}{{32}}} $
 $ \dfrac{{{r_1}}}{{{r_2}}} = \sqrt {\dfrac{1}{{16}}} $
 $ \dfrac{{{r_1}}}{{{r_2}}} = \dfrac{1}{4} $
Therefore, the ratio of diffusion rate of oxygen to hydrogen is $ 1:4 $ .
Hence, the correct option is (a) $ 1:4 $ .

Additional Information:
Diffusion can be classified into two main types: Simple diffusion and facilitated diffusion. Simple diffusion is known as a process in which the substance moves through a semipermeable membrane without any help from transport proteins. Bacteria deliver small nutrients, oxygen and water into the cytoplasm through simple diffusion. Facilitated diffusion is known as a passive movement of molecules across the cell membrane from the region of higher concentration to the region of lower concentration by means of a carrier molecule.

Note :
Graham's Law says that the effusion rate of a gas is inversely proportional to the square root of the mass of its particles. The diffusion rate depends on various factors such as the concentration gradient (the increase or decrease in concentration from one point to another); the amount of surface area available for diffusion; and also, the distance the gas particles must travel.